1. Field of the Invention
The present invention relates to an adaptive equalizer for use in digital cellular receiver terminals or the like, and more particularly to an adaptive equalizer capable of compensating for a deterioration in the channel characteristics which results from a carrier frequency offset.
2. Description of the Related Art
Heretofore, land mobile communications systems, typically automobile telephone system, have been analog communications systems. To meet demands for a rapid increase in the number of subscribers to such land mobile communications systems, more diverse types of data to be transmitted, and compatibility with ISDN (Integrated-Services Digital Network), efforts are being made to develop digital mobile communications systems.
For example, the Telecommunication Industries Association in the U.S.A. established in 1989 the digital automobile telephone standards which are summarized as follows:
Frequency band: 800/900 MHz
Access method: TDMA
Audio encoding method: 13 kbps VSELP
Number of channels per wave: 3
Carrier interval: 60 kHz (30 kHz interleave)
Modulation method: .pi./4-shift DQPSK
Base station radius: 0.5.about.20 km
A .pi./4-shift DQPSK (.pi./4-shift differentially encoded quadrature phase shift keying) signal is a signal which is produced by differentially encoding symbols to be transmitted and then subjecting them to .pi./4-shift QPSK.
The process of .pi./4-shift QPSK will be described below. The differentially encoding process that has no effect on an understanding of the present invention will not be described below.
In .pi./4-shift QPSK, a series of bits of digital signals 0 and 1 is divided into pairs of bits, and the phase angle .theta..sub.k of a high-frequency sine wave is determined depending on one of 2-bit combinations 00, 01, 10, 11 (a 2-bit combination {X.sub.k, Y.sub.k } is referred to as a "symbol"). A sine wave S(t) having a phase angle .theta..sub.k corresponding to the kth symbol is expressed by: EQU S(t)=cos (.omega..sub.c t+.theta..sub.k)k=1, 2, 3, 4 (-T/2.ltoreq.t.ltoreq.T/2) (1)
where EQU .theta..sub.k =.+-..pi./4, .+-.3.pi./4 (2),
.omega..sub.c is the angular frequency of a carrier sine wave (if a carrier frequency is f.sub.c, then .omega..sub.c =2.pi.f.sub.c), and
T is the duration of one symbol.
The sine wave S(t) may also be expressed as follows: EQU S(t)=a.sub.k cos (.omega..sub.c t)+b.sub.k sin (.omega..sub.c t)(3)
where EQU (a.sub.k, b.sub.k)=(1/.sqroot.2,1/.sqroot.2), (-1/.sqroot.2,1/.sqroot.2), (-1/.sqroot.2,-1/.sqroot.2), (1/.sqroot.2,-1/.sqroot.2) (4) EQU a.sup.2 +b.sup.2 =1 (5).
The values of (a.sub.k, b.sub.k) represent the components of a symbol on an I-Q rectangular Cartesian coordinate plane composed of an in-phase axis (I axis) and a quadrature axis (Q axis).
FIG. 8 of the accompanying drawings shows, by way of example, a conventional digital cellular receiver for receiving QPSK-modulated waves. It is assumed that the digital cellular receiver has received a signal R(t) that is expressed by: EQU R(t)=a' cos (.omega..sub.c t)+b' sin (.omega..sub.c t) (6)
where (a', b') is (a.sub.k, b.sub.k) that has been received (the suffix k is omitted).
In the digital cellular receiver shown in FIG. 8, the received signal R(t) expressed by the equation (6) is subjected to quadrature detection to reproduce the combinations (a.sub.k, b.sub.k) (and further to determine phase differences between succeeding combinations (a.sub.k, b.sub.k) in differential decoding) thereby reproducing the symbols, and then demodulate the symbols into a series of bits 0 and 1 which is original serial signals.
The quadrature detector divides the received signal expressed by the equation (6) into two signals, multiplies one of the signal by a sine wave cos(.omega..sub.c t) which is of the same frequency and phase as the transmitted carrier, and multiplies the other signal by a sine wave sin(.omega..sub.c t). This quadrature detection process is called a synchronous detection process. The results of the process are given as follows: EQU R(t) cos (.omega..sub.c t)=(1/2)(a'+a' cos 2.omega..sub.c t+b' sin 2.omega..sub.c t) (7),
and EQU R(t) sin (.omega..sub.c t)=(1/2)(b'-b' cos 2.omega..sub.c t+a' sin 2.omega..sub.c t) (8).
The signals expressed by the above equations (7) and (8) are passed through a low-pass filter to remove multiple frequency components therefrom, thus obtaining (1/2)a', (1/2)b'.
In the above synchronous detection process, however, it is necessary to generate a carrier whose frequency and phase are equal to those of the transmitted carrier. Methods of extracting and reproducing such a carrier in a receiver generally include inverse modulation, multiplication, and Costas loop. These methods reproduce a carrier based on waveform information contained in the received signal. Therefore, if the received signal has a distorted waveform due to multipath fading, for example, then they fail to extract and reproduce a carrier with high accuracy. Under such an adverse condition, the synchronous detection process cannot be relied upon.
In conventional digital communications between stationary stations, there has been employed an adaptive equalizer to compensate for a decoding error rate because they are also susceptible to multipath fading. FIG. 9 of the accompanying drawings illustrates, for example, an adaptive equalizer in the digital communication terminal shown in FIG. 8.
An output signal (a', b') from the synchronous detector is inputted to a demultiplexer which selects a signal of its own slot and sends it to the adaptive equalizer.
As shown in FIG. 9, the adaptive equalizer comprises a filter unit composed of a feed-forward filter and a feedback filter for processing a complex input signal whose real part is the I component of the output signal from the synchronous detector and imaginary part is the Q component of the output signal from the synchronous detector, the feed-forward and feedback filters having complex coefficients, a decision unit for determining the phase of an output signal from the filter unit, a complex adder for calculating an equalization error signal, a coefficient updating unit for updating the coefficients of the feed-forward and feedback filters based on the equalization error signal according to an algorithm, and a training signal generator for training the adaptive equalizer.
The input signal (a', b') is filtered by the filter unit to remove a waveform distortion due to multipath fading therefrom, and then sent to the decision unit. If it is assumed that the filter unit outputs a signal (a.sub.of, b.sub.of), then the decision unit determines which phase of the equation (4) the output signal from the filter unit corresponds to, and outputs a signal (a.sub.dec, b.sub.dec) corresponding to the phase. The complex adder determines the difference (a.sub.of -a.sub.dec, b.sub.of -b.sub.dec) between the output signal (a.sub.of, b.sub.of) from the filter unit and the output signal (a.sub.dec, b.sub.dec) from the decision unit, and outputs the difference as an equalization error signal. The coefficient updating unit updates the coefficients of the feed-forward and feedback filters. The output signal (a.sub.dec, b.sub.dec) from the decision unit is fed back to the feedback filter. The adaptive equalizer of this type is referred to as a decision feedback equalizer, which is known to be effective in compensating for a delay dispersion of a received signal due to multipath fading.
Digital mobile communication devices are more susceptible to multipath fading than conventional digital communication devices for use between stationary stations because they are often required to communicate with each other in locations such as between buildings or the like in cities. Therefore, the receivers of digital mobile communication terminals should be equipped with an oscillator for generating a detecting carrier to carry out detection (quasi-synchronous detection) similar to the synchronous detection using the oscillated detecting carrier.
Since the frequency of the transmitted carrier is known, the oscillator in the receiver is required to generate a carrier having the same frequency as the frequency of the transmitted carrier. However, such a requirement may not necessarily be met. It is also impossible to eliminate the phase difference. In the quasi-synchronous detection, therefore, it is necessary to effect quadrature detection using the detecting carrier whose frequency and phase are slightly different from those of the transmitted carrier, for reproducing a transmitted series of symbols.
The quadrature detector for carrying out the quasi-synchronous detection divides the received signal expressed according to the equation (6) into two signals, multiplies one of the signals by a sine wave cos(.omega.'t+.theta.), and multiplies the other signal by a sine wave sin(.omega.'t+.theta.), where .omega.' is the angular frequency of the detecting carrier which is different from the frequency of the transmitted carrier, and .theta. the phase difference between the detecting carrier and the transmitted carrier. The signals produced by the above multiplication are passed through a low-pass filter, which outputs the following signals: EQU R(t) cos (.omega.'t+.theta.).fwdarw.(1/2)[a' cos (.DELTA..omega.t+.theta.)-b' sin (.DELTA..omega.t+.theta.)](9) EQU R(t) sin (.omega.'t+.theta.).fwdarw.(1/2)[a' sin (.DELTA..omega.t+.theta.)+b' cos (.DELTA..omega.t+.theta.)](10)
where .DELTA..omega. is the difference between the transmitted carrier .omega..sub.c and the detecting carrier .omega.', and called a carrier offset.
As can be seen from the equations (9) and (10), the signal (a', b') produced as a result of the quasi-synchronous detection is expressed as a vector, on the I-Q plane, whose absolute value is (1/2)(a'.sup.2 +b'.sup.2).sup.1/2 and which keeps rotating at an angular velocity .DELTA..omega.. While the vector (a', b') is rotating, if the angular velocity .DELTA..omega. exceeds about 10 Hz, then the error rate is large with the normal decoding process. Therefore, it is necessary to detect and compensate for a carrier offset with some means.
The manner in which the adaptive equalizer responds to a carrier offset will be described below.
If an input signal produced by quadrature detection of a signal which is received by the receiver and applied to the adaptive equalizer contains a carrier offset .DELTA..omega., then the spectrum Reql(.omega.) of the input signal is represented by: EQU Reql(.omega.)=W(.omega.-.DELTA..omega.)G((.omega.-.DELTA..omega.)H(.omega.- .DELTA..omega.) (11)
where W(.omega.) is the spectrum of a transmitted series of symbols w.sub.i, H(.omega.) the spectrum of an impulse response h(t) of the transmission path, and G(.omega.) the spectrum of an impulse response g(g) of the waveform shaping filter. These spectrums are frequency-shifted by the carrier offset .DELTA..omega.. Since the filter unit of the adaptive equalizer realizes a transfer function 1/{G(.omega.-.DELTA..omega.)H(.omega.-.DELTA..omega.)} to equalize the input signal, it produces an output signal: ##EQU1## The spectrum of the received symbols is shifted by the carrier offset .DELTA..omega.. An inverse Fourier transform of the output signal is expressed by: EQU Ofil(.omega.)=w.sub.i exp{j .DELTA..omega.t}
where i=0, 1, 2, 3, . . . EQU iT.ltoreq.t&lt;(i+1)T
T: symbol interval (sec).
Therefore, the received symbols in the output signal from the filter unit rotate at the angular velocity .DELTA..omega. without stopping at rest, and hence the equalization error signal contains the carrier offset .DELTA..omega..
Accordingly, even the adaptive equalizer cannot compensate for the carrier offset. It is one of the tasks to be achieved in developing digital mobile communications receivers to provide appropriate means for compensating for a carrier offset.